Question

What does the word conserved mean as applied to the law of conservation of energy?

Short answer

Conserved means that the total energy remains constant in a closed system, as per the law of conservation of energy.

Step-by-step solution

Understanding the Concept of Conservation

The term 'conservation' in physics refers to a quantity that remains constant over time. It signifies that the quantity is neither lost nor gained but stays the same - it is 'conserved.'

Applying Conservation to Energy

When we say energy is conserved, it means the total energy in a closed system remains constant. No matter the processes that occur within the system, the total amount of energy does not change.

Law of Conservation of Energy Statement

The law states that energy cannot be created or destroyed in an isolated system. It can only be transformed from one form to another. For example, potential energy can be transformed into kinetic energy and vice versa, but the total energy remains the same.

Clarification with Examples

Consider a pendulum. At its highest point, the energy is all potential. As it swings down, potential energy is converted to kinetic energy. Despite this transformation, the sum of potential and kinetic energy remains constant, illustrating conservation of energy.

Key concepts

Conservation

In the realm of physics, "conservation" is a term that denotes something remains unchanged over time. When we apply this idea to energy, it means that the total amount of energy in a system does not vary. This remains true despite various transformations that energy might undergo. For instance, in a cooking process, the heat from the stove is transformed into the energy that heats the food. Yet, if we sum up all the energy used and produced, it will equal the initial amount of energy, hence it is conserved.
Understanding conservation helps us grasp that energy will always 'be there,' consistently manifesting in different forms but never dimming into nothingness.

Closed System

A closed system is central to the discussion of energy conservation. In physics, a closed system is one where no energy crosses the boundary of the system. It neither gains nor loses energy to the surrounding environment.
Such a system allows us to apply the law of conservation of energy accurately. For example:

• An insulated thermos with hot soup can be considered a closed system if it perfectly prevents heat loss.
• A sealed jar where no air enters or leaves is another example of a closed system.

By maintaining the same amount of energy within the system, we can track how energy transforms without external influence, guaranteeing that the total energy remains constant.

Energy Transformation

Energy is remarkably versatile; it can shift from mechanical to thermal, chemical to electrical, and beyond. This ability to transform is crucial in our daily lives and technological advancements.
Consider a hydroelectric plant:

• The potential energy of stored water in a dam is converted to kinetic energy as the water flows down.
• This kinetic energy is then transformed into mechanical energy via turbines.
• Finally, mechanical energy is converted to electrical energy that powers our homes.

Despite these transformations, if we calculate the total energy at each stage, it remains the same, proving conservation of energy through transformation.

Potential Energy

Potential energy is the stored energy in an object due to its position or configuration. It is energy waiting to be unleashed.
Potential energy is observed in various forms, such as:

• The gravitational potential energy of an object at height, like a book placed on a shelf.
• Elastic potential energy in a compressed spring.
• Chemical potential energy stored in fuels and batteries.

When released, potential energy can transform into other types of energy, like kinetic energy when the book falls, yet the total energy stays consistent in a closed system.

Kinetic Energy

Kinetic energy is the energy of motion. Any object that moves, from a rolling ball to flowing water, possesses kinetic energy. It is calculated using the formula \( KE = \frac{1}{2} mv^2 \), where \( m \) represents mass and \( v \) velocity.
When kinetic energy transforms to other forms, such as when a moving car comes to a stop and its kinetic energy turns into heat, the energy isn't lost. Instead, it simply changes form, thereby maintaining the conservation of energy principle. This transformation and the intrinsic conservation ensure energy's persistence and recyclability across different modes.